the change in the points of research is very slow. plus 1. I tried to set the maximum high, the change is the same.

Right, the base rate of change for planetary meters is +/- 1 per turn (except for population, which has a more complex formula). Certain techs can increase the rate of change for certain meters. Meters having a max (like planet defense) will always be capped by that max, so switching from defense focus to something else can cause a big swing, not just -1/turn.

the course is very long. the first two in the area of 5 minutes. further up to 30 minutes.

I don't understand what you are talking about there.

does not save when exiting. saving is every move, you can not save it manually. inactive button.

The game does autosave when exiting, unless you've disabled that or force the game to terminate before the save is complete. The default is once per turn, but you can adjust that in the Options. At the very start of a turn the save button is inactive while the AI's are preparing their orders, which are needed for the save. Late in the game that can take a while, but it will become active again.

If I provided any code, scripts or other content here, it's released under GPL 2.0 and CC-BY-SA 3.0

I assume you mean the time to resolve a turn (between hitting "TURN" and being able to play next turn).
What are your computer specs? CPU/processor, RAM/memory, GPU/graphics, operating system...
What are the galaxy settings of your current game? Number of planetary systems, number of AI players...

Then you should curb your expectations. Your CPU is not fast nor has good parallel performance.

Try a game with 150 systems and 6 opponents. 40 opponents means 40 threads of AI processing, that's probably your main bottleneck here.
If turn processing is fine with 6 opponents you can try more, but I recommend finishing a game like that first to see how does it behaves on late game (when turns require much more processing than at the start of a game). If that happens, you can try with less systems (usually 15-25 per player).

Side note: the galaxy generation algorithm has some minimum number of systems per opponent, I think it's 5 (maybe 10), so a game with 40 opponents (plus you) is at least 205 systems.

You'll get that each planetary meter of Industry or Research will increase (or decrease) by 3 (instead of 1) each turn.

This will make every planet to reach its current maximum value faster, but you won't notice a great speed up of the game pace in general.
If what you want is to be able to get technologies and finish ships faster, there is an option in the GUI that you can adjust before starting a game, to make technologies and items cost more or less points. I'm sorry I can't start FreeOrion in this computer to show you an screenshot, but I think it is easy to fine, in the screen where you configure the galaxy (number of stars, opponents, etc.).

Also, you can change the base production and research you get from population, defined in the file /default/scripting/common/base_prod.macros. Change the INDUSTRY_PER_POP and RESEARCH_PER_POP values for greater ones to get more PPs and RPs from your planets.